What is the x-intercept of the graph of the function f(x)=x^2-16+64

Recall that y = 0 at the x-intercept(s) of a function.

Thus, set f(x)=x^2-16x+64 = 0 and solve for x.

Notice that x^2-16x+64 is the square of x-8, so x^2-16x+64 = 0 = (x-8)^2 = 0.

Take the square root of both sides: √0 = √ [ (x-8)^2 ]

Then x-8 = 0, and x = 8. Note that this equation has TWO real, equal roots: {8,8}.